Postscript Phase Space Generators

Here are some phase portrait generators for a few Hamiltonian systems,
and the programs are written in . . . Postscript!
The postscript files contain the numerical computations along
with formatting routines, so all you need to do is send the file
to the printer and let it do all the work.

Each file includes documentation in the comments, and there are a number of
parameters that can be set at the top of the file. The parameters
should be self-explanatory, but one parameter of note is the color
vs. black/white option, which should be set correctly, since the
color setting does not look as nice on a greyscale printer.
Additionally, for the continuous-time systems, the integrator method
and stepsize must be set to ensure an accurate phase space.

Note that these files can take a very long time to print, especially
on older printers. For example, the standard map file with the settings
here takes
6 minutes on a Hewlett Packard 4500N color laser printer, 17 minutes
on an Apple Laserwriter 12/640 PS, and 45 minutes on a Hewlett Packard
Laserjet 4MP. You can reduce the time to print by selecting fewer points
for output or rasterizing the postscript on a fast computer (using
Ghostview or Acrobat Distiller) before sending the job to the printer.

Standard Map:

The
standard map postscript file.
This system is also known as the kicked rotor system, where
a particle moves in a one-dimensional,
cosinusoidal potential with the time dependence of a sequence
of periodic delta functions.

Continuous-Time Systems:

The simplest example here is the
pendulum postscript file,
which uses 4th-order Runge-Kutta (fixed step) to do
the integration, which works well since this system is
not especially taxing on the integrator.

A more interesting example is the
"sin2" system, which
is similar to the kicked rotor, but the potential
has a sin2(t) time dependence.
This time dependence results in a family of three primary
resonances: one at p=0 and the others at
p=±2p.
A time-shifted variation on this phase space is the
cos2 system, where the
system is sampled at the temporal peaks of the potential rather
than the minima.
A further variation on this system is the
"reduced sin2" system,
where the sin2 pulses have a (possibly) shorter duty cycle.
These examples include the option to use either Runge-Kutta
or Stoermer integrators (both with fixed steps); the Stoermer
method seems much more efficient for these problems.